28,134 research outputs found
A vector quantization approach to universal noiseless coding and quantization
A two-stage code is a block code in which each block of data is coded in two stages: the first stage codes the identity of a block code among a collection of codes, and the second stage codes the data using the identified code. The collection of codes may be noiseless codes, fixed-rate quantizers, or variable-rate quantizers. We take a vector quantization approach to two-stage coding, in which the first stage code can be regarded as a vector quantizer that “quantizes” the input data of length n to one of a fixed collection of block codes. We apply the generalized Lloyd algorithm to the first-stage quantizer, using induced measures of rate and distortion, to design locally optimal two-stage codes. On a source of medical images, two-stage variable-rate vector quantizers designed in this way outperform standard (one-stage) fixed-rate vector quantizers by over 9 dB. The tail of the operational distortion-rate function of the first-stage quantizer determines the optimal rate of convergence of the redundancy of a universal sequence of two-stage codes. We show that there exist two-stage universal noiseless codes, fixed-rate quantizers, and variable-rate quantizers whose per-letter rate and distortion redundancies converge to zero as (k/2)n -1 log n, when the universe of sources has finite dimension k. This extends the achievability part of Rissanen's theorem from universal noiseless codes to universal quantizers. Further, we show that the redundancies converge as O(n-1) when the universe of sources is countable, and as O(n-1+ϵ) when the universe of sources is infinite-dimensional, under appropriate conditions
Mutually Uncorrelated Primers for DNA-Based Data Storage
We introduce the notion of weakly mutually uncorrelated (WMU) sequences,
motivated by applications in DNA-based data storage systems and for
synchronization of communication devices. WMU sequences are characterized by
the property that no sufficiently long suffix of one sequence is the prefix of
the same or another sequence. WMU sequences used for primer design in DNA-based
data storage systems are also required to be at large mutual Hamming distance
from each other, have balanced compositions of symbols, and avoid primer-dimer
byproducts. We derive bounds on the size of WMU and various constrained WMU
codes and present a number of constructions for balanced, error-correcting,
primer-dimer free WMU codes using Dyck paths, prefix-synchronized and cyclic
codes.Comment: 14 pages, 3 figures, 1 Table. arXiv admin note: text overlap with
arXiv:1601.0817
Pegasus: A New Hybrid-Kinetic Particle-in-Cell Code for Astrophysical Plasma Dynamics
We describe Pegasus, a new hybrid-kinetic particle-in-cell code tailored for
the study of astrophysical plasma dynamics. The code incorporates an
energy-conserving particle integrator into a stable, second-order--accurate,
three-stage predictor-predictor-corrector integration algorithm. The
constrained transport method is used to enforce the divergence-free constraint
on the magnetic field. A delta-f scheme is included to facilitate a
reduced-noise study of systems in which only small departures from an initial
distribution function are anticipated. The effects of rotation and shear are
implemented through the shearing-sheet formalism with orbital advection. These
algorithms are embedded within an architecture similar to that used in the
popular astrophysical magnetohydrodynamics code Athena, one that is modular,
well-documented, easy to use, and efficiently parallelized for use on thousands
of processors. We present a series of tests in one, two, and three spatial
dimensions that demonstrate the fidelity and versatility of the code.Comment: 27 pages, 12 figures, accepted for publication in Journal of
Computational Physic
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